Towards efficient SimRank computation on large networks

SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores

Modeling the AgInSbTe Memristor

The AgInSbTe memristor shows gradual resistance tuning characteristics, which makes it a potential candidate to emulate biological plastic synapses. The working mechanism of the device is complex, and both intrinsic charge-trapping mechanism and extrinsic electrochemical metallization effect are confirmed in the AgInSbTe memristor. Mathematical model of the AgInSbTe memristor has not been given before. We propose the flux-voltage controlled memristor model. With piecewise linear approximation technique, we deliver the flux-voltage controlled memristor model of the AgInSbTe memristor based on the experiment data. Our model fits the data well. The flux-voltage controlled memristor model and the piecewise linear approximation method are also suitable for modeling other kinds of memristor devices based on experiment data

Physical modeling and validation of porpoises' directional emission via hybrid metamaterials

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Dong, E., Zhang, Y., Song, Z., Zhang, T., Cai, C., & Fang, N. X. Physical modeling and validation of porpoises' directional emission via hybrid metamaterials. National Science Review, 6(5), (2019): 921-928, doi:10.1093/nsr/nwz085.In wave physics and engineering, directional emission sets a fundamental limitation on conventional simple sources as their sizes should be sufficiently larger than their wavelength. Artificial metamaterial and animal biosonar both show potential in overcoming this limitation. Existing metamaterials arranged in periodic microstructures face great challenges in realizing complex and multiphase biosonar structures. Here, we proposed a physical directional emission model to bridge the gap between porpoises’ biosonar and artificial metamaterial. Inspired by the anatomical and physical properties of the porpoise's biosonar transmission system, we fabricated a hybrid metamaterial system composed of multiple composite structures. We validated that the hybrid metamaterial significantly increased directivity and main lobe energy over a broad bandwidth both numerically and experimentally. The device displayed efficiency in detecting underwater target and suppressing false target jamming. The metamaterial-based physical model may be helpful to achieve the physical mechanisms of porpoise biosonar detection and has diverse applications in underwater acoustic sensing, ultrasound scanning, and medical ultrasonography.E.D., Y.Z., Z.S., T.Z. and C.C. acknowledge the financial support in part by the National Key Research and Development Program of China (2018YFC1407504), the National Natural Science Foundation of China (41676023, 41276040 and 41422604). N.X.F. acknowledges the support from the MIT Energy Initiative grant. Z.S. thanks the China Scholarship Council for the financial support of his oversea study in Woods Hole Oceanographic Institution

Accurate numerical solution to the finite-size Dicke model

By using extended bosonic coherent states, a new technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in literature. Finite-size scaling for several observables, such as the ground-state energy, Berry phase, and concurrence are analyzed. The existing discrepancy for the scaling exponent of the concurrence is reconciled.Comment: 4 pages, 5 figures. Phys. Rev. A (in press, a Rapid Communication

Quantum transport in a curved one-dimensional quantum wire with spin-orbit interactions

The one-dimensional effective Hamiltonian for a planar curvilinear quantum wire with arbitrary shape is proposed in the presence of the Rashba spin-orbit interaction. Single electron propagation through a device of two straight lines conjugated with an arc has been investigated and the analytic expressions of the reflection and transmission probabilities have been derived. The effects of the device geometry and the spin-orbit coupling strength $\alpha$ on the reflection and transmission probabilities and the conductance are investigated in the case of spin polarized electron incidence. We find that no spin-flip exists in the reflection of the first junction. The reflection probabilities are mainly influenced by the arc angle and the radius, while the transmission probabilities are affected by both spin-orbit coupling and the device geometry. The probabilities and the conductance take the general behavior of oscillation versus the device geometry parameters and $\alpha$. Especially the electron transportation varies periodically versus the arc angle $\theta_{w}$. We also investigate the relationship between the conductance and the electron energy, and find that electron resonant transmission occurs for certain energy. Finally, the electron transmission for the incoming electron with arbitrary state is considered. For the outgoing electron, the polarization ratio is obtained and the effects of the incoming electron state are discussed. We find that the outgoing electron state can be spin polarization and reveal the polarized conditions.Comment: 7 pages, 8 figure